Question

In the arithmetic sequence the first term is $8$, the common difference is $4$, and the sum of the first $n$ terms is $2808$. Find the value of $n$.

• A. $31$
• B. $36$
• C. $78$
• D. $41$

Answer 1

The correct option is B $36$

in arithmetic series,

first term is $a=8$

common difference is $d=4$

$t_n=a+(n-1)d$

Sum of arithmetic series of n terms is

$\frac{n}{2}(t_1+t_n)\Rightarrow \frac{n}{2}(a+a+(n-1\left)d\right)=2808$

$\Rightarrow \frac{n}{2}(2\times 8+(n-1)\times 4)=2808\Rightarrow (4n+12)n=2808\times 2\Rightarrow n^2+3n-1404=0$

so $n=36$